 Solution

The conserved total angular momentum is ${\mathbf{J}}_t=(0,0,2)$, and the black-hole spin magnitude isThe initial hole is noncollinear with the total vector, so persistent positive alignment torque leads to the positive $z$ direction. The final vectors areThe final disk magnitude is $2-\sqrt{3}$, smaller than its initial magnitude one, and its direction is parallel to the hole. Their sum remains $(0,0,2)$.